A probabilistic solution to the AX=XB problem: Sensor calibration without correspondence

Abstract

The "AX=XB" sensor calibration problem is ubiquitous in the fields of robotics and computer vision. In this problem A, X, and B are each homogeneous transformations (i.e., rigid-body motions) with A and B given from sensor measurements, and X is the unknown that is sought. For decades this problem is known to be solvable for X when a set of exactly measured compatible A's and B's with known correspondence is given. However, in practical problems, it is often the case that the data streams containing the A's and B's will present at different sample rates, they will be asynchronous, and each stream may contain gaps in information. Practical scenarios in which this can happen include hand-eye calibration and ultrasound image registration. We therefore present a method for calculating the calibration transformation, X, that works for data without any a priori knowledge of the correspondence between the As and Bs. © 2013 Springer-Verlag.